Relation To Independence
Random variables X, Y are independent if and only if the conditional distribution of Y given X is equal to the unconditional distribution of Y. For discrete random variables: P(Y = y | X = x) = P(Y = y) for all relevant x and y. For continuous random variables having a joint density: fY(y | X=x) = fY(y) for all relevant x and y.
Read more about this topic: Conditional Probability Distribution
Famous quotes containing the words relation to, relation and/or independence:
“The foregoing generations beheld God and nature face to face; we, through their eyes. Why should not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us, and not the history of theirs?”
—Ralph Waldo Emerson (1803–1882)
“There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.”
—Ralph Waldo Emerson (1803–1882)
“We must have constantly present in our minds the difference between independence and liberty. Liberty is a right of doing whatever the laws permit, and if a citizen could do what they forbid he would no longer be possessed of liberty.”
—Charles Louis de Secondat Montesquieu (1689–1755)